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International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD)

Simulations of 2D Maxwell-Bloch equations

Jingyi Xiong, Max Colice, Friso Schlottau, Kelvin H. Wagner, Bengt Fornberg B

Published Sep 1, 2007• 0 citations
Publisher

Abstract

Rare-earth-doped crystals can be modelled as inhomogeneously broadened two-level atoms. Beam propagation in the crystals can be described by the Maxwell-Bloch equations. We numerically solve Maxwell's equations by using the FFT-finite difference beam propagation method and the Bloch equations by using the finite difference method. Numerical simulation results are given for an off-axis 3-pulse photon echo.

DOI
10.1109/nusod.2007.4348996

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Rare-earth-doped crystals can be modelled as inhomogeneously broadened two-level atoms. Beam propagation in the crystals can be described by the Maxwell-Bloch equations. We numerically solve Maxwell's equations by using the FFT-finite difference beam propagation method and the Bloch equations by using the finite difference method. Numerical simulation results are given for an off-axis 3-pulse photon echo.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium.The convergence and stability of this numerical method are proved by comparing with the analytic solutions and area theorem derived under special condition.The simulations of arbitrary conditions is discussed by employing this method and analyze the pulse evolution for different detunings,relaxation times and inhomogeneously broadened linewidthes.The established numerical method provides a good way to have further study about the coherent interaction of short optical pulses with resonant mediums,and can be used to solve the corrections of Maxwell-Bloch equations.
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Important applications in optical information storage and processing based on photon echo have been developed.An accurate and effective numerical method to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium will be introduced.Two-pulse photon echo is calculated then photon echo and multiple-pulse photon echoes are stimulated in optical thin(thick) media by using the method,and the physical properties of those echoes are analyzed.The results show that the approach to storage and retrieval of light using multiple-pulse photon echoes based on stimulated photon echo is an effective mode.
This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works. The influence of thickness on the three-pulse photon echo’s amplitude and efficiency is analyzed with the Maxwell–Bloch equations solved by finite-difference time-domain method. We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm 3 + :YAG when the attenuation of the input pulse is taken into account. Meanwhile, we find the expression 0.09 exp ⁡ ( α ′ L ) , which is previously employed to describe the relationship between echo’s efficiency and thickness, should be modified as 1.3 ⋅ 0.09 exp ⁡ ( 2.4 ⋅ α ′ L ) with the propagation of echo considered.
A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.